class_docstr: Create a linear Information filter. Information filters
  compute the
  inverse of the Kalman filter, allowing you to easily denote having
  no information at initialization.
  
  You are responsible for setting the various state variables to reasonable
  values; the defaults below will not give you a functional filter.
  
  Parameters
  ----------
  
  dim_x : int
      Number of state variables for the  filter. For example, if you
      are tracking the position and velocity of an object in two
      dimensions, dim_x would be 4.
  
      This is used to set the default size of P, Q, and u
  
  dim_z : int
      Number of of measurement inputs. For example, if the sensor
      provides you with position in (x,y), dim_z would be 2.
  
  dim_u : int (optional)
      size of the control input, if it is being used.
      Default value of 0 indicates it is not used.
  
  self.compute_log_likelihood = compute_log_likelihood
  self.log_likelihood = math.log(sys.float_info.min)
  
  
  Attributes
  ----------
  x : numpy.array(dim_x, 1)
      State estimate vector
  
  P_inv : numpy.array(dim_x, dim_x)
      inverse state covariance matrix
  
  x_prior : numpy.array(dim_x, 1)
      Prior (predicted) state estimate. The *_prior and *_post attributes
      are for convienence; they store the  prior and posterior of the
      current epoch. Read Only.
  
  P_inv_prior : numpy.array(dim_x, dim_x)
      Inverse prior (predicted) state covariance matrix. Read Only.
  
  x_post : numpy.array(dim_x, 1)
      Posterior (updated) state estimate. Read Only.
  
  P_inv_post : numpy.array(dim_x, dim_x)
      Inverse posterior (updated) state covariance matrix. Read Only.
  
  z : ndarray
      Last measurement used in update(). Read only.
  
  R_inv : numpy.array(dim_z, dim_z)
      inverse of measurement noise matrix
  
  Q : numpy.array(dim_x, dim_x)
      Process noise matrix
  
  H : numpy.array(dim_z, dim_x)
      Measurement function
  
  y : numpy.array
      Residual of the update step. Read only.
  
  K : numpy.array(dim_x, dim_z)
      Kalman gain of the update step. Read only.
  
  S :  numpy.array
      Systen uncertaintly projected to measurement space. Read only.
  
  log_likelihood : float
      log-likelihood of the last measurement. Read only.
  
  likelihood : float
      likelihood of last measurment. Read only.
  
      Computed from the log-likelihood. The log-likelihood can be very
      small,  meaning a large negative value such as -28000. Taking the
      exp() of that results in 0.0, which can break typical algorithms
      which multiply by this value, so by default we always return a
      number >= sys.float_info.min.
  
  inv : function, default numpy.linalg.inv
      If you prefer another inverse function, such as the Moore-Penrose
      pseudo inverse, set it to that instead: kf.inv = np.linalg.pinv
  
  
  Examples
  --------
  
  See my book Kalman and Bayesian Filters in Python
  https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python
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docstr: State Transition matrix
docstr_tok: ["State","Transition","matrix"]
code: def F(self):
      """State Transition matrix"""
      return self._F
  
file_path: filterpy/filterpy/kalman/information_filter.py
imports: from __future__ import absolute_import, division
  from copy import deepcopy
  import math
  import sys
  import numpy
  from numpy import dot, zeros, eye
  from filterpy.stats import logpdf
  from filterpy.common import pretty_str, reshape_z
label_desc: Use image node_id 5 for calling the InformationFilter obj's underlying member method code with example usage: obj.F() and returns: self